<PAGE>   1
                                    FORM 10-Q

                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D. C. 20549

(Mark One)

[X]          QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15 (d) OF THE
                         SECURITIES EXCHANGE ACT OF 1934

For the quarterly period ended                March 31, 1999
                              --------------------------------------------------

                                       OR

[ ]        TRANSITION REPORT PURSUANT TO SECTION 13 OR 15 (d) OF THE
                         SECURITIES EXCHANGE ACT OF 1934

For the transition period from                      to
                              ----------------------  --------------------------


Commission file number               1-737
                      ----------------------------------------------------------


                            TEXAS PACIFIC LAND TRUST
--------------------------------------------------------------------------------
             (Exact name of registrant as specified in its charter)


              NOT APPLICABLE                                   75-0279735
--------------------------------------------------------------------------------
(State or other jurisdiction of incorporation                 (I.R.S. Employer
             or organization)                                Identification No.)

              80 Broad Street, Suite 2700, New York, New York 10004
--------------------------------------------------------------------------------
                    (Address of principal executive offices)
                                   (Zip Code)


                                  212/269-2266
--------------------------------------------------------------------------------
              (Registrant's telephone number, including area code)


                                 NOT APPLICABLE
--------------------------------------------------------------------------------
              (Former name, former address and former fiscal year,
                          if changed since last report)


Indicate by check mark whether the registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during
the preceding 12 months (or for such shorter period that the registrant was
required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days.

Yes   X    No
    -----     -----



<PAGE>   2




                                     Part I

                              FINANCIAL INFORMATION
                            TEXAS PACIFIC LAND TRUST
                                 BALANCE SHEETS
                      MARCH 31, 1999 and DECEMBER 31, 1998
                                               


<TABLE>
<CAPTION>
                                                                                                March 31,            December 31,
               ASSETS                                                                              1999                    1998
                                                                                               -----------           -----------
                                                                                               (Unaudited) 
<S>                                                                                            <C>                   <C>        
Cash                                                                                           $   153,905           $   147,375
Temporary cash investments at-cost which approximates market                                     2,125,000             2,450,000
Accounts receivable                                                                                262,681               255,544
Accrued interest receivable                                                                        432,203               408,486
Prepaid expenses                                                                                    28,742                41,059
Notes receivable for land sales                                                                  9,773,221            11,006,307
Real estate acquired through foreclosure:
      (26,413.09 acres at March 31, 1999 and 26,450.63 acres at December 31, 1998)               4,652,873             4,422,078
Water wells, leasehold improvements, furniture and
       equipment - at cost less accumulated depreciation                                           121,509               125,565

Property, no value assigned :
     Land (surface rights) situated in twenty-one counties in
         Texas - 1,032,980.22 acres in 1999 and 1,034,386.64 acres in 1998                              --                    --

     Town lots in Iatan, Loraine and Morita - 628 lots in 1999 and 1998                                 --                    --

     1/16 nonparticipating perpetual royalty interest in 386,987.70 acres in 1999 and 1998              --                    --

     1/128 nonparticipating perpetual royalty interest in 85,413.60 acres in 1999 and 1998              --                    --
                                                                                               -----------           -----------
                                                                                               $17,550,134           $18,856,414
                                                                                               ===========           ===========

                LIABILITIES AND CAPITAL

Federal income taxes                                                                           $   663,785           $   348,311
Other taxes                                                                                         84,298                16,854
Other liabilities                                                                                   19,483                 2,064
Escrow deposits on land sales                                                                        5,000                 7,000
Deferred taxes                                                                                   4,497,319             4,840,479
                                                                                               -----------           -----------
          Total liabilities                                                                      5,269,885             5,214,708

Capital:
      Certificates of Proprietary Interest, par value $100
            each; outstanding one certificate in 1999 and 1998                                          --                    --

      Sub-share Certificates in Certificates of Proprietary Interest, par value
            $.16 2/3 each; outstanding 2,650,905 sub-shares in 1999 and
            2,669,805 sub-
            shares in 1998                                                                              --                    --

      Net proceeds from all sources                                                             12,280,249            13,641,706
                                                                                               -----------           -----------
           Total capital                                                                        12,280,249            13,641,706

                                                                                               -----------           -----------
                                                                                               $17,550,134           $18,856,414
                                                                                               ===========           ===========
</TABLE>


                 See accompanying notes to financial statements.


                                       (1)


<PAGE>   3

                            TEXAS PACIFIC LAND TRUST
                              STATEMENTS OF INCOME

                                   (Unaudited)


<TABLE>
<CAPTION>
                                                                                         Three Months Ended
                                                                                             March 31
                                                                                   -----------------------------
                                                                                      1999               1998
                                                                                   ----------         ----------
<S>                                                                                <C>                <C>       
Income:
     Rentals, royalties and sundry income                                          $1,157,050         $1,465,516
     Land sales                                                                        77,021          1,879,400
     Interest                                                                         260,618            244,834
                                                                                   ----------         ----------
                                                                                    1,494,689          3,589,750
                                                                                   ----------         ----------

Expenses:
     Taxes, other than Federal income taxes                                           103,547            124,418
     General and administrative expenses                                              352,537            347,643
                                                                                   ----------         ----------
                                                                                      456,084            472,061
                                                                                   ----------         ----------

            Income before provision for
                 Federal income taxes                                               1,038,605          3,117,689

Provision for Federal income taxes                                                    322,420            976,036
                                                                                   ----------         ----------

                 Net income                                                        $  716,185         $2,141,653
                                                                                   ==========         ==========

Average number of sub-share certificates
       and equivalent sub-share certificates
       outstanding                                                                  2,665,888          2,750,988
                                                                                   ==========         ==========

Earnings per sub-share certificate                                                 $      .27         $      .78
                                                                                   ==========         ==========

Cash dividend per sub-share certificate                                            $      .40         $      .40
                                                                                   ==========         ==========
</TABLE>


                 See accompanying notes to financial statements.


                                       (2)


<PAGE>   4


                            TEXAS PACIFIC LAND TRUST
                            STATEMENTS OF CASH FLOWS

                                   (Unaudited)


<TABLE>
<CAPTION>
                                                                                        Three Months Ended
                                                                                            March 31
                                                                                   ----------------------------
                                                                                       1999            1998
                                                                                   -----------      -----------
<S>                                                                                <C>              <C>
Cash flows from operating activities:

    Net income                                                                     $   716,185      $ 2,141,653

        Adjustments to reconcile net income to net cash provided by operating
            activities:

                 Depreciation                                                           10,800           28,500
                 Deferred taxes                                                       (343,160)         279,504

                 (Increase) decrease in assets:
                    Accounts receivable                                                 (7,137)             518
                    New notes receivable from land sales                               (51,750)      (1,329,000)
                    Payments received on notes receivable                            1,064,510          434,858
                    Foreclosed notes receivable journaled to other real estate         220,326             --
                    Accrued interest receivable                                        (23,717)         (35,184)
                    Prepaid expenses                                                    12,317           13,650
                    Real estate acquired through foreclosure                          (230,795)            --
                 Increase (decrease) in liabilities:
                    Federal income taxes                                               315,474          652,406
                    Other taxes payable                                                 67,444           72,722
                    Escrow deposits on land sales                                       (2,000)           2,000
                    Other liabilities                                                   17,419           93,415
                                                                                   -----------      -----------

                        Total adjustments                                            1,049,731          213,389
                                                                                   -----------      -----------

                            Net cash provided by operating activities                1,765,916        2,355,042
                                                                                   -----------      -----------

Cash flows from investing activities-
   Additions to water wells, leasehold improvements,
          furniture and equipment                                                       (6,744)          (6,869)


Cash flows from financing activities:
    Sub-shares purchased for retirement                                             (1,010,440)        (614,945)
    Dividends paid                                                                  (1,067,202)      (1,102,802)
                                                                                   -----------      -----------

                         Net cash used by financing activities                      (2,077,642)      (1,717,747)

Net (decrease) increase in cash and cash equivalents                                  (318,470)         630,426

Cash and cash equivalents at beginning
    of year                                                                          2,597,375        1,912,591
                                                                                   -----------      -----------
Cash and cash equivalents at end
    of period                                                                      $ 2,278,905      $ 2,543,017
                                                                                   ===========      ===========
</TABLE>


                 See accompanying notes to financial statements.



                                       (3)



<PAGE>   5


                            TEXAS PACIFIC LAND TRUST
                          NOTES TO FINANCIAL STATEMENTS
                                 MARCH 31, 1999



(1)      In the opinion of management, the accompanying unaudited financial
         statements contain all adjustments (consisting of only normal
         recurring accruals) necessary to present fairly the financial position
         of Texas Pacific Land Trust (Trust) as of March 31, 1999 and the
         results of its operations and its cash flows for the three months
         ended March 31, 1999 and March 31, 1998, respectively. These financial
         statements and footnotes included herein should be read in conjunction 
         with the Trust's annual financial statements as of December 31, 1998 
         and 1997 and for each of the years in the three year period ended 
         December 31, 1998 included in the Trust's Form 10-K.

(2)      No value is assigned to the land, unless acquired through foreclosure;
         consequently, no allowance for depletion is computed, and no charge to
         income is made therefore, and no cost is deducted from the proceeds of
         the land sales in computing gain or loss thereon.

(3)      The Sub-shares and the Certificates of Proprietary Interest are freely
         interchangeable in the ratio of one Certificate of Proprietary Interest
         for 600 Sub-shares or 600 Sub-shares for one Certificate of Proprietary
         Interest.

(4)      The Trust's effective Federal income tax rate is less than the 34%
         statutory rate because taxable income is reduced by statutory
         percentage depletion allowed on mineral royalty income.

(5)      The results of operations for the three months ended March 31, 1999 are
         not necessarily indicative of the results to be expected for the full 
         year.

(6)      Cash in excess of daily requirements is invested in money market
         instruments with maturities of ninety days or less. Such investments
         are deemed to be cash equivalents for purposes of the statements of
         cash flows.

         Supplemental cash flow information for the three months ended March
         31,1999 and 1998 is summarized as follows:


<TABLE>
<CAPTION>
                                                     1999            1998
                                                   --------        --------
<S>                                                <C>             <C>     
         Federal income taxes paid                 $350,106        $ 44,126
                                                   ========        ========
</TABLE>


         There were no non-cash investing and financing activities during the
         three months ended March 31, 1999 and 1998.

(7)      In June 1997, the Financial Accounting Standards Board (FASB) issued
         SFAS No. 131, Disclosures about segments of an Enterprise and Related
         Information. SFAS No. 131 establishes standards for the way public
         business enterprises are to report information about operating
         segments. SFAS No. 131 utilizes the management approach as a basis for
         identifying reportable segments. The management approach is based on
         the way that management organizes the segments within the enterprise
         for making operating decisions and assessing performance. The Trust's
         management views its operations as one segment and believes the only
         significant activity is managing the land which was conveyed to the
         Trust in 1888. Trust Management makes decisions about resource
         allocation and performance assessment based on the same financial
         information presented in these financial statements. Managing the land
         includes sales and leases of such land, and the retention of oil and
         gas royalties.

                                       (4)


<PAGE>   6
(8)      Effective January 1, 1999, the Trust implemented the provisions of
         Statement of Position (SOP) 98-5, Reporting on the Cost of Start-Up
         Activities. SOP 98-5 requires that the costs of start-up activities,
         including organizational costs, be expensed as incurred. SOP 98-5,
         requires initial application to be recorded as of the beginning of the
         fiscal year in which the SOP is first adopted and is reported as the
         cumulative effect of a change in accounting principle. Due to the
         nature of the Trust's operations, the effect of implementation of this
         new pronouncement had no effect on the financial condition or results
         of operations of the Company.











                                      (5)
<PAGE>   7


                           Management's Discussion and
                       Analysis of Financial Condition and
                          Results of Operations for the
                               Three Months Ended
                             March 31, 1999 and 1998


Results of Operations for Quarter Ended March 31, 1999 Compared to Quarter Ended
March 31, 1998

Earnings per sub-share were $.27 for the first quarter of 1999 compared to $.78
for the first quarter of 1998. Total revenues were $1,494,689 compared to
$3,589,750, a decrease of 58.4%.

The Trust sold 1,446 acres of land for a total of $77,021, an average of $53
per acre in the first quarter of 1999. This compares to 23,688 acres at an
average price of $79 per acre for a total of $1,879,400 in the first quarter of
1998.

Land Sales may vary widely from year to year and quarter to quarter. The total
dollar amount, the average price per acre, and the number of acres sold in any
one year or quarter should not be assumed to be indicative of land sales in the
future. The Trust is a passive seller of land; it does not actively solicit
sales of land. The demand for and the sales price of any particular tract of the
Trust's land is influenced by many factors including the national and local
economies, the rate of residential and commercial development in nearby areas,
livestock carrying capacity, and the conditions of the local agricultural
industry which itself is influenced by range conditions and prices for livestock
and other agricultural products. Approximately 99% of the Trust's land is
classified as ranch land and intermingled with other ownerships to form ranching
units. Ranch land sales are, therefore, largely dependent on the actions of the
adjoining landowners.

Rentals, royalties and sundry income were $1,157,050 in the first quarter of
1999 compared to $1,465,516 in the first quarter of 1998, a decrease of 21.0%.

Oil and gas royalty revenue was $463,843, down 38.6% compared to the first
quarter of 1998. Oil royalty revenue was $281,713, down 44.7% compared to 1998.
Crude oil production subject to the Trust's royalty interest was down 14.0% in
the first quarter and the average price per royalty barrel was down 35.6%
compared to 1998. Gas royalty revenue was $182,130 in the first quarter, down
25.9% on a volume decrease of 2.8% and a price decrease of 23.9%.

Easement and Sundry income was $605,434 down 2.8% from the first quarter of
1998, but considered to be exceptionally high as easement and seismic permit
income were up for the first quarters of 1999 and 1998. Both seismic permit and
easement income are not predictable sources of income.

Interest revenue increased 6.4% in the first quarter of 1999 compared to 1998.
Interest from notes receivable was $223,548 an increase of 6.1% over the first
quarter of 1998. Notes receivable were $9,773,221 as of March 31, 1999 down 4.2%
from March 31, 1998. Sundry interest was $37,070, up 8.6% over the first quarter
of 1998.

Taxes, other than Federal income taxes were down 16.8% from the first quarter of
1998. This is due to decrease in land inventory and decrease in oil and gas
royalty production taxes. 

General and administrative expenses were increased 1.4% compared to the first 
quarter of 1998.

Liquidity and Capital Resources

The Trust's oil and gas royalty revenues, lease rentals and receipts of interest
and principal on notes receivable has generated more than adequate amounts of
cash to meet the Trust's needs and should continue to do so in the predictable
future.


                                       (6)
<PAGE>   8


Management's Discussion (cont'd)

Year 2000 Issue

The Trust recognizes that the arrival of the Year 2000 poses a unique challenge
to the ability of an entity's information technology system and non-information
technology systems to recognize the date change from December 31, 1999 to
January 1, 2000. As of March 31, 1999, the Trust has assessed and made certain
changes to provide for continued functionality of its systems. An assessment of
the readiness of the Trust's external entities, such as vendors, customers,
payment systems and others is ongoing. Due to the nature and extent of the
Trust's operations that are effected by Year 2000 issues, the Trust does not
believe that Year 2000 issues will have a material adverse effect on the
business operation or the financial performance of the Trust. There can be no
assurance, however, that Year 2000 issues will not adversely effect the Trust or
its business. The Trust believes that the cost to make appropriate changes to
its internal and external systems will not be significant and that such costs
will be funded completely through operations.

Words or phrases when used in this Form 10-Q or other filings with the 
Securities and Exchange Commission, such as "does not believe" and "believes",
or similar expressions are intended to identify "forward-looking statements"
within the meaning of the Private Securities Litigation Reform Act of 1995.

                         Quantitative and Qualitative
                         Disclosures About Market Risk

There have been no material changes in the information related to market risk
of the Trust since December 31, 1998.


                                       (7)

<PAGE>   9


                                     PART II


                                OTHER INFORMATION


Item 6.   Exhibits and Reports on Form 8-K

(a)  Exhibits. Interim report furnished to shareholders upon request per sub-
     part Item 601 (19) Regulation S-K.

     Exhibit 27 - Financial Data Schedule.

(b)  Reports on Form 8-K. The registrant has filed no reports on Form 8-K during
     the quarter for which this report is filed.






                                   SIGNATURES

         Pursuant to the requirements of the Securities Exchange Act of 1934,
the registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.



                                                 TEXAS PACIFIC LAND TRUST
                                          --------------------------------------
                                                       (Registrant)



Date May 13, 1999                       By /s/ ROY THOMAS
    ---------------------------------     --------------------------------------
                                          Roy Thomas, General Agent, 
                                          Authorized Signatory and Principal
                                          Financial Officer



                                       (8)

<PAGE>   10


                               INDEX TO EXHIBITS


<TABLE>
<CAPTION>
EXHIBIT
NUMBER                        EXHIBIT
------                        -------
<S>                           <C>
  27                          Financial Data Schedule
</TABLE>